Session C7: Undergraduate Research/SPS III

Guiding brine shrimp through mazes by solving reaction diffusion equations.

Excitable systems driven by reaction diffusion equations have been shown to not only find solutions to mazes but to also to find the shortest path between the beginning and the end of the maze. In this talk we describe how we can use the Fitzhugh-Nagumo model, a generic model for excitable media, to solve a maze by varying the basin of attraction of its two fixed points. We demonstrate how two dimensional mazes are solved numerically using a Java Applet and then accelerated to run in real time by using graphic processors (GPUs). An application of this work is shown by guiding phototactic brine shrimp through a maze solved by the algorithm. Once the path is obtained, an Arduino directs the shrimp through the maze using lights from LEDs placed at the floor of the Maze. This method running in real time could be eventually used for guiding robots and cars through traffic.   

An Agent Based Model for Social Class Emergence

We present an open system agent-based model to analyze the effects of education and the society-specific wealth transactions on the emergence of social classes. Building on previous studies, we use realistic functions to model how years of education affect the income level. Numerical simulations show that the fraction of an individual’s total transactions that is invested rather than consumed can cause wealth gaps between different income brackets in the long run. In an attempt to incorporate the network effects, we also explore how the probability of interactions among agents depending on the spread of their income brackets affects wealth distribution.   

Generation and characterization of high-density gas jets from a 150 micron diameter nozzle in air

This work characterizes argon and nitrogen gas jets in unconventional atmospheric pressure instead of the conventional vacuum pressure, and then compares the results directly to that of the conventional technique of creating gas jet targets. A Mach-Zehnder interferometer was used to estimate the number density of the gas jet, and a Rayleigh scattering setup was used to determine if either of the techniques formed atomic clusters and if so, estimating relative quantity. The diameter of the cylindrical nozzle used for is around 150 $\mu $m with backing pressures ranging from 13 bars to 69 bars. The highest backing pressure gives us a maximum phase shift value of 9 rad, number density 4.5 \texttimes 10$^{20}$ cm$^{-3}$. Another characteristic property of these jets is the shock diamond formation due to the flows interaction with atmospheric air particles. The highest number density for a shock diamond was \textasciitilde 10$^{20}$ cm$^{-3}$ which does not necessarily occur at higher backing pressure. Also, the distance from the first shock diamond to the nozzle orifice does increase with increasing backing pressure, consistent with a theory. This type of high-density, thin gas jets can be used as a laser target for creating dense plasmas and producing energetic particles and X-rays in the atmospheric conditions.   

Combination Gravimetric/Volumetric Sorption Instrument for Energy Applications.

The use of gaseous fuels such as hydrogen and methane (natural gas) will reduce emissions. Unfortunately, the storage of hydrogen and methane at room temperature is difficult because they are both supercritical gases, making the adoption of these fuels cumbersome. One means of overcoming the storage problem is to use physisorption-based systems which exploit the van der Waals interaction between the gas and a nanoporous material to compress the gases to near liquid densities. To measure the amount of gas in these materials, gravimetric or volumetric methods are employed. Gravimetric weighs the amount of gas and volumetric uses differences in gas pressures. Gravimetric systems typically have problems with buoyancy corrections. Volumetric systems normally have larger uncertainties that propagate through the isotherm. A modified system will be presented which allows for both gravimetric and volumetric gas sorption measurements. Additionally, the buoyancy corrections for the gravimetric measurements are significantly small and less than the uncertainties in the measurement. This apparatus can take measurements of most gases at room temperature and up to 200 bar.   

Decoherence of nitrogen-vacancy defect spins in diamond from surface spins

In recent work[1,2], researchers measured the spin coherence time of intentionally-doped nitrogen-vacancy (NV) spin ensembles. The spin coherence times of these spins depends on their local environment, including their nearness to the surface of the material. We calculated the decoherence time of a deep spin within the material affected by the presence of a sheet of surface spins interacting with the deep spin through the dipolar interaction. These calculations describe the experimental measurements qualitatively, however quantitative agreement requires the assumption these spins extend deeper into the material from the surface layer. [1] J. Cardellino et al., Nat. Nanotechnol. 9, 343 (2014) [2] K. Ohno et al., Appl. Phys. Lett. 101, 082413 (2012). This work was supported by the NIGMS under Award Number R25GM058939   

Electrostatic Simulation of Charge Trapping in Carbon Nanotube Vertical Organic Field Effect Transistors

The carbon nanotube vertical organic field effect transistor is a vertical sequence consisting of a gate electrode, gate dielectric, thin nanotube network source electrode, organic semiconducting channel and finally the drain electrode. The drain current is modulated by the gate voltage which varies a Schottky barrier between source and channel layers. Hysteresis in the current-voltage characteristic has been observed when a electret charge trapping layer is placed between the nanotube source and the gate dielectric. We provide a model for charge injection into a trapping layer placed in contact with the carbon nanotube film and solve self-consistently for the electrostatics and the occupancy of the traps. For a range of applied gate voltages the simulations demonstrate hysteresis of the carbon nanotubes' charge as a result of the electric field produced by the trapped charge. This affects the current by modulating the Schottky barrier.   

Quantum correlations of magnetic impurities by a multiple electron scattering in carbon nanotubes

In this work we analyze the quantum correlations and polarizations states of magnetic impurities spins, when a multiple electron scattering was taken place. A sequence of non-correlated electrons interacts through scattering producing quantum correlation which will have an impact on the electronic transmission. We consider a short range Heisenberg interaction between ballistic electron and static impurities. We analyze the cases when the electron scattering is produce by one and two impurities, obtaining the electronic transmission rates. Concurrence and fidelity calculations are performed to obtain the level of quantum entanglement and polarization correlations. We also discuss the possible application of this model to metallic and semiconductor carbon nanotubes, which could have important implications on spintronics and quantum information devices.   

Exact Diagonalization of a Quantum XXZ Model with Long-Range Interactions

In recent years, rapid advancement has been made in using ultra-cold gases as quantum spin simulators, with two dimensional lattices becoming a rich target for exploring the exotic states and excitations of spin-1/2 systems on frustrated lattices. When the interaction in the system becomes long-ranged, the spins are frustrated by the long-range interaction. Consequently, the competition between the geometric frustration and the long-range interaction results in the the underlying orders present in the ground state being unclear. Here, we investigate the quantum dipolar XXZ model with exact diagonalization to characterize and contrast the ground state and excitations on square and triangular lattices to provide a baseline for comparison with experiments.   

The Configuration Space Symmetries in the Quantum Bouncer

We study a few-body particle system with contact interactions in a quantum bouncer potential well. In principle, the strength of the gravitational field can be extracted from the one-particle energy spectrum, but this is currently experimentally impractical. This project explores how varying the number of particles and tuning the particle interaction strength can improve measurement sensitivity. The analysis exploits the additional symmetries of configuration space that occur either in the unitary limit of contact interactions or when the bouncer potential is decorated with additional infinite delta-barriers.   

Exploring Quantum Dynamics of Continuous Measurement with a Superconducting Qubit

Weak measurements obtain partial information about a quantum state with minimal backaction. This enables state tracking without immediate collapse to eigenstates, of interest to both experimental and theoretical physics. State tomography and continuous weak measurements may be used to reconstruct the evolution of a single system, known as a quantum trajectory. We examine experimental trajectories of a two-level system at varied measurement strengths with constant unitary drive. Our analysis is applied to a transmon qubit dispersively coupled to a 3D microwave cavity in the circuit QED architecture. The weakly coupled cavity acts as pointer system for QND measurements in the qubit’s energy basis. Our results indicate a marked difference in state purity between two approaches for trajectory reconstruction: the Bayesian and Stochastic Master Equation (SME) formalisms. Further, we observe the transition from diffusive to jump-like trajectories, state purity evolution, and a novel, tilted form of the Quantum Zeno effect. This work provides new insight into quantum behavior and prompts further comparison of SME and Bayesian formalisms to understand the nature of quantum systems. Our results are applicable to a variety of fields, from stochastic thermodynamics to quantum control.   

A simple table-top experiment demonstrating mechanical oscillation of a macroscopic object driven by radiation pressure.

We have implemented a Michelson's interferometer to demonstrate the resonant motion of a cm-sized cantilever due to radiation pressure of a laser diode (5 mW or less). The mechanical oscillation is found to be 2.454 ($+$/-0.003) kHz and is independently confirmed by dynamic force microscopy in which a piezoelectric transducer (PZT) is employed as a mechanical driver. We will discuss other applications, such as a wavelength meter and short-ranged force measurements, based on our simple table-top experiment.   

Transient even and odd order nonlinearity of a YBCO transmission line

Second (IMD2) and third (IMD3) order intermodulation distortions were found to exhibit dependencies on temperature and magnetic field. A carrier wave at the 890 MHz resonant frequency of the type-II YBa$_{\mathrm{2}}$Cu$_{\mathrm{3}}$O$_{\mathrm{7-\delta }}$ superconducting resonator circuit, with T$_{\mathrm{C}}=$89K, was introduced into the circuit via an electric coupling antenna. Two off-resonance probe signals were injected into the circuit via a separate magnetic coupling element. The combination of these three signals locally excited synchronous second and third order IMD. A static magnetic field was applied perpendicularly to the film which induced magnetic flux vortices in the sample. Upon removal of the static magnetic field, IMD2 and IMD3 exhibited distinct transient decay modes correlating to temperature. Between 85.0K and 87.5K, IMD3 decayed exponentially. Above 87.5K, IMD3 exhibited bounded exponential growth, while within a narrow temperature range around 87.5K, removal of a static magnetic field strongly suppressed IMD3. IMD2 exhibited exponential decay at all temperatures. Even and odd order microwave nonlinearities were thus shown to result from different, magnetically coupled, physical mechanisms.   

Magnetic Levitation Experiments with the Electrodynamic Wheel

Our experiments explored inductive magnetic levitation using circular Halbach arrays with the strong variable magnetic field on the outer rim of the ring. Such a system is usually called an Electrodynamic Wheel (EDW). Rotating this wheel around a horizontal axis above a flat conducting surface should induce eddy currents in said surface through the variable magnetic flux. The eddy currents produce, in turn, their own magnetic fields which interact with the magnets of the EDW. We constructed two Electrodynamic Wheels with different diameters and demonstrated that the magnetic interactions produce both lift and drag forces on the EDW which can be used for levitation and propulsion of the EDW. The focus of our experiments is the direct measurement of lift and drag forces to compare with theoretical models using wheels of two different radii.